norm(x)>=constant is not a convex constraint. The fact that your constraint is trivial because constant=0 is a coincidence.
i thought all norms are convex
convex_expression <= constraint is a convex constraint.
convex_expression >= 0 is non-convex.
Also, norm(affine_expression) is convex, but norm(non_affine_expression) is not necessarily.
Please read http://cvxr.com/cvx/doc/basics.html#constraints and if you have the energy, read and work exercises in https://web.stanford.edu/~boyd/cvxbook/